Finding an unknown angle
We know that ∠1 and ∠2 are complementary angles. That means, they shape together a straigth line, then
∠1 + ∠2 = 90°
Since they have a ratio of 4:5 we can say that
∠1 = 4x and
∠2 = 5x
Then, using the first formula
∠1 + ∠2 = 90°
4x + 5x = 90°
We solve for x:
4x + 5x = 90°
↓ 4x + 5x = 9x
9x = 90°
↓ dividing by 9 both sides
x = 10°
Since
∠1 = 4x is the smaller angle, replacing x by 10°:
∠1 = 4x
∠1 = 4 · 10°
∠1 = 40°
Answer: the measure of the smaller angle is 40°